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Hamilton was born in 1936 in Cairo, Egypt, the second of seven children. His father A. M. Hamilton was a New Zealand-born engineer. His mother B. M. Hamilton was a medical doctor, also from New Zealand.

The Hamilton family settled in Kent. During the Second World War, the young Hamilton was evacuated to Edinburgh. He had an interest in natural history from an early age and would spend his spare time collecting butterflies and other insects. In 1946 he discovered E.B. Ford's New Naturalist book Butterflies, which introduced him to the principles of evolution by natural selection, genetics and population genetics.

He was educated at Tonbridge School, where he was in Smythe House. As a 12-year old he was seriously injured while playing with explosives his father had. These were left over from his making hand grenades for the British Home Guard during World War II; the accident might have killed him if his mother had not been a doctor. The boy had to have a thoracotomy in King's College Hospital to save his life, but fingers on his right hand had to be amputated and he was left with scarring on his body. He needed six months to recover.

Hamilton stayed on an extra term at Tonbridge to complete the Cambridge entrance examinations, and then travelled in France. He completed two years of national service. As an undergraduate at St. John's College, he was uninspired by the "many biologists [who] hardly seemed to believe in evolution". He was intrigued by Ronald Fisher's book The Genetical Theory of Natural Selection; but Fisher lacked standing at Cambridge as he was viewed as only a statistician. Hamilton was excited by Fisher's chapters on eugenics. In earlier chapters, Fisher provided a mathematical basis for the genetics of evolution. Working through the stodgy prose, Hamilton later blamed Fisher's book for his getting only a 2:1 degree.

Both Fisher and J. B. S. Haldane had seen a problem in how organisms could increase the fitness of their own genes by aiding their close relatives, but not recognised its significance or properly formulated it. Hamilton worked through several examples, and eventually realised that the number that kept falling out of his calculations was Sewall Wright's coefficient of relationship. This became Hamilton's rule: in each behaviour-evoking situation, the individual assesses his neighbour's fitness against his own according to the coefficients of relationship appropriate to the situation. Algebraically, the rule posits that a costly action should be performed if:

Where C is the cost in fitness to the actor, r the genetic relatedness between the actor and the recipient, and B is the fitness benefit to the recipient. Fitness costs and benefits are measured in fecundity. His two 1964 papers entitled The Genetical Evolution of Social Behavior are now widely referenced.

The proof and discussion of its consequences, however, involved detailed mathematics, and two reviewers passed over the paper. The third, John Maynard Smith, did not completely understand it either, but recognised its significance. Having his work passed over later led to friction between Hamilton and Maynard Smith, as Hamilton thought Smith had held his work back to claim credit for the idea (during the review period Maynard Smith published a paper that referred briefly to similar ideas). The Hamilton paper was printed in the Journal of Theoretical Biology and, when first published, was largely ignored. Recognition of its significance gradually increased to the point, and it is now routinely cited in biology books. Although the theory can be proven mathematically, to date no empirical studies have calculated values for R, B, and C to determine if Hamilton's rule is ever satisfied in nature. After more than 40 years, some scientists claim that the theory remains unconfirmed, although predictions based upon it are largely supported. Because B and C represent gains and losses, it is impossible to compare actual gains and losses with the possible ones that would result from an alternate history. Statisticians, however, argue that such comparisons can be made between similar families in which different versions of history play out.

Much of the discussion relates to the evolution of eusociality in insects of the order Hymenoptera (ants, bees and wasps) based on their unusual haplodiploid sex-determination system. This system means that females are more closely related to their sisters than to their own (potential) offspring. Thus, Hamilton reasoned, a "costly action" would be better spent in helping to raise their sisters, rather than reproducing themselves.

In his 1970 paper Selfish and Spiteful Behaviour in an Evolutionary Model Hamilton considers the question of whether harm inflicted upon an organism must inevitably be a byproduct of adaptations for survival. What of possible cases where an organism is deliberately harming others without apparent benefit to the self? Such behaviour Hamilton calls spiteful. It can be explained as the increase in the chance of an organism's genetic alleles to be passed to the next generations by harming those that are less closely related than relationship by chance.

Spite, however, is unlikely ever to be elaborated into any complex forms of adaptation. Targets of aggression are likely to act in revenge, and the majority of pairs of individuals (assuming a panmictic species) exhibit a roughly average level of genetic relatedness, making the selection of targets of spite problematic.

Between 1964 and 1978 Hamilton was a lecturer at University College London. Whilst there he published a paper in Science on "extraordinary sex ratios". Fisher (1930) had proposed a model as to why "ordinary" sex ratios were nearly always 1:1 (but see Edwards 1998), and likewise extraordinary sex ratios, particularly in wasps, needed explanations. Hamilton had been introduced to the idea and formulated its solution in 1960 when he had been assigned to help Fisher's pupil A.W.F. Edwards test the Fisherian sex ratio hypothesis. Hamilton combined his extensive knowledge of natural history with deep insight into the problem, opening up a whole new area of research.

The paper was also notable for introducing the concept of the "unbeatable strategy", which John Maynard Smith and George R. Price were to develop into the evolutionarily stable strategy (ESS), a concept in game theory not limited to evolutionary biology. Price had originally come to Hamilton after deriving the Price equation, and thus rederiving Hamilton's rule. Maynard Smith later peer reviewed one of Price's papers, and drew inspiration from it. The paper was not published but Maynard Smith offered to make Price a co-author of his ESS paper, which helped to improve relations between the men. Price committed suicide in 1975, and Hamilton and Maynard Smith were among the few present at the funeral.[4]

Hamilton was regarded as a poor lecturer. This shortcoming would not affect the popularity of his work, however, as it was popularised by Richard Dawkins in Dawkins' 1976 book The Selfish Gene.

In 1966 he married Christine Friess and they were to have three daughters, Helen, Ruth and Rowena. 26 years later they amicably separated.

"Well, in our country," said Alice, still panting a little, "you'd generally get to somewhere else—if you ran very fast for a long time, as we've been doing."

"A slow sort of country!" said the Queen. "Now, here, you see, it takes all the running you can do, to keep in the same place. If you want to get somewhere else, you must run at least twice as fast as that!" (Carroll, pp. 46)

This theory hypothesizes that sex evolved because new and unfamiliar combinations of genes could be presented to parasites, preventing the parasite from preying on that organism: species with sex were able to continuously "run away" from their parasites. Likewise, parasites were able to evolve mechanisms to get around the organism's new set of genes, thus perpetuating an endless race.

The field of social evolution, of which Hamilton's rule has central importance, is broadly defined as being the study of the evolution of social behaviours, i.e. those that impact on the fitness of individuals other than the actor. Social behaviours can be categorized according to the fitness consequences they entail for the actor and recipient. A behaviour that increases the direct fitness of the actor is mutually beneficial if the recipient also benefits, and selfish if the recipient suffers a loss. A behaviour that reduces the fitness of the actor is altruistic if the recipient benefits, and spiteful if the recipient suffers a loss. This classification was first proposed by Hamilton in 1964.[citation needed]

Through his collaboration with Hugh N. Comins and Bob May on evolutionarily stable dispersal strategies, Hamilton acquired an Erdős number of 5.[6]

During the 1990s Hamilton became increasingly interested in the controversial argument that the origin of HIV lay in oral polio vaccines trials conducted by Hilary Koprowski in Africa during the 1950s. Letters by Hamilton on the topic to the major peer-reviewed journals were rejected. To look for indirect evidence of the OPV hypothesis by assessing natural levels of SIV in primates, in early 2000 he and two others ventured on a field trip to the war-torn Democratic Republic of the Congo.

He returned to London from Africa on 29 Jan 2000. He was admitted to University College Hospital London on 30 Jan 2000. He was transferred to Middlesex Hospital London on 5 Feb 2000 and died there on 7 Mar 2000. An inquest was held on 10 May 2000 at Westminster Coroner's Court to inquire into rumours about the cause of his death. The coroner concluded that his death was due to "Multi-organ failure due to upper gastrointestinal haemorrhage due to a duodenal diverticulum and arterial bleed through a mucosal ulcer".[8]

I will leave a sum in my last will for my body to be carried to Brazil and to these forests. It will be laid out in a manner secure against the possums and the vultures just as we make our chickens secure; and this great Coprophanaeus beetle will bury me. They will enter, will bury, will live on my flesh; and in the shape of their children and mine, I will escape death. No worm for me nor sordid fly, I will buzz in the dusk like a huge bumble bee. I will be many, buzz even as a swarm of motorbikes, be borne, body by flying body out into the Brazilian wilderness beneath the stars, lofted under those beautiful and un-fused elytra which we will all hold over our backs. So finally I too will shine like a violet ground beetle under a stone.

”

The second volume of his collected papers, Evolution of Sex, was published in 2002, and the third and final volume, Last Words, in 2005.

Hamilton started to publish his collected papers starting in 1996, along the lines of Fisher's collected papers, with short essays giving each paper context. He died after the preparation of the second volume, so the essays for the third volume come from his coauthors.